On the realization of discrete cosine transform using the distributed arithmetic

Algorithm for p/sup m/-length discrete cosine transform

“…Recently, we found that it is possible to realize a prime length DCT through two half-length cyclic correlations, which results in avery regular structure. Hence, it is very suitable for VLSI implementation [2,3].…”

A new VLSI algorithm and architecture for the hardware implementation of type IV discrete cosine transform using a pseudo-band correlation structure

“…The rationale for this fact is that the data flow plays a central role in designing a VLSI architecture. Thus, the use of regular and modular computational structures such as cyclic convolution and circular correlation [7][8][9][10] has been proved to offer good implementation solutions for the discrete transforms using systolic arrays [11] and distributed-arithmetic [12]. They lead to efficient VLSI implementations with low I/O cost and reduced hardware complexity, high speed and a regular and modular hardware structure.…”

On the theoretical lower bound of the multiplicative complexity for DCT

“…In [3], we proved that any DCT of odd prime size P can be decomposed into one fP-1V2-point cyclic convolution and one (P-IVz-point skew-cyclic convo:ution at no cost of multiplication. As the minimum number of factorial polynomials of the polynomial z(p-1)!2-1 is 2, that implies 2P-5 real multiplications are required for the realization of the P-point DCT.…”

“…Hence, though some of the development in this paper refer to correlations, they apply equally well to convolutions. Second, theoretical minimum multiplicative requirements for the realization of the DCT are derived based on the modification of the results and the algorithm proposed in [3] respectively. Then we will provide some short length DCT algorithms based on the derived results and some other effective DCT algorithms[SJ, which support the PFM algorithm [6] with reduced arithmetic complexity.…”

“…In this paper, we will show that the same lower bound can be derived by two entirely different approaches. In particular, one of them is based on the algorithm proposed in [3] while another one is based on a modification of the results of the algorithm proposed in [4].…”